# Problem 260: Stone Game

![graphic](img260.gif)

A game is played with three piles of stones and two players. At her
turn, a player removes one or more stones from the piles. However, if
she takes stones from more than one pile, she must remove the same
number of stones from each of the selected piles. In other words, the
player chooses some N>0 and removes: N stones from any single pile;
or N stones from each of any two piles (2N total); or N stones from each
of the three piles (3N total). The player taking the last stone(s) wins
the game. A winning configuration is one where the first player can
force a win. For example, (0,0,13), (0,11,11) and (5,5,5) are winning
configurations because the first player can immediately remove all
stones. A losing configuration is one where the second player can force
a win, no matter what the first player does. For example, (0,1,2) and
(1,3,3) are losing configurations: any legal move leaves a winning
configuration for the second player. Consider all losing configurations
(xi,yi,zi) where xi ≤ yi ≤ zi ≤ 100. We can verify that Σ(xi+yi+zi) =
173895 for these. Find Σ(xi+yi+zi) where (xi,yi,zi) ranges over the
losing configurations with xi ≤ yi ≤ zi ≤ 1000.